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 A086792 Orders of finite groups G with the property that the sum of the orders of all the proper normal subgroups of G equals the order of G. 1
 6, 12, 28, 30, 56, 360, 364, 380, 496, 760, 792, 900, 992, 1224, 1656, 1680, 1980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The only Abelian groups with this property are the cyclic groups C_n where n is a perfect number, so this sequence can be seen as a groups analogy of perfect numbers. Derek Holt (mareg(AT)mimosa.csv.warwick.ac.uk) computed the orders of the non-Abelian groups in the sequence up to n=500 and commented "In general, if 2^n - 1 is a Mersenne prime, then 2^(n-1)*(2^n - 1) is a perfect number and the group with presentation < x,y | x^(2^n-1) = 1, y^(2^n) = 1, y^-1 x y = x^-1 > has order equal to the sum of the orders of its proper normal subgroups." So if n is an even perfect number, 2n also belongs to this sequence (the numbers 12 and 56 above). LINKS Tom Leinster, Perfect numbers and groups Tom De Medts, Attila Maróti, Perfect numbers and finite groups Tom De Medts, Leinster groups Sci.math, Groups analogy of perfect numbers CROSSREFS Cf. A000396. Sequence in context: A009242 A032647 A327165 * A064987 A057341 A068412 Adjacent sequences:  A086789 A086790 A086791 * A086793 A086794 A086795 KEYWORD nonn,more AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 04 2003 EXTENSIONS a(10)-a(17) added using "Leinster groups" link by Eric M. Schmidt, May 02 2014 STATUS approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)